Generalised spectral dimensions in non-perturbative quantum gravity

Abstract

The seemingly universal phenomenon of scale-dependent effective dimensions in non-perturbative theories of quantum gravity has been shown to be a potential source of quantum gravity phenomenology. The scale-dependent effective dimension from quantum gravity has only been considered for scalar fields. It is however possible that the non-manifold like structures, that are expected to appear near the Planck scale, have an effective dimension that depends on the type of field under consideration. To investigate this question, we have studied the spectral dimension associated to the Laplace-Beltrami operator generalised to $k$-form fields on spatial slices of the non-perturbative model of quantum gravity known as Causal Dynamical Triangulations. We have found that the two-form, tensor and dual scalar spectral dimensions exhibit a flow between two scales at which an effective dimension appears. However, the one-form and vector spectral dimensions show only a single effective dimension. The fact that the one-form and vector spectral dimension do not show a flow of the effective dimension can potentially be related to the absence of a dispersion relation for the electromagnetic field, but dynamically generated instead of as an assumption.

arXiv comment35 pages, 18 figures

References in corpus (23)

• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe
• Emergence of a 4D World from Causal Quantum Gravity
• Reconstructing the Universe
• Nonperturbative Quantum Gravity
• Quantum Gravity from Causal Dynamical Triangulations: A Review
• The Nonperturbative Quantum de Sitter Universe
• Dimension and Dimensional Reduction in Quantum Gravity
• Discrete Exterior Calculus
• Renormalization Group Flow in CDT
• Quantum gravity and gravitational-wave astronomy
• Gravitational-wave luminosity distance in quantum gravity
• Geometry of the quantum universe
• Impact of topology in causal dynamical triangulations quantum gravity
• The phase structure of Causal Dynamical Triangulations with toroidal spatial topology
• Laplacians on discrete and quantum geometries
• The higher-order spectrum of simplicial complexes: a renormalization group approach
• Searching for a continuum limit in causal dynamical triangulation quantum gravity
• Spectral dimensions and dimension spectra of quantum spacetimes
• Properties of dynamical fractal geometries in the model of Causal Dynamical Triangulations
• Topology induced first-order phase transitions in lattice quantum gravity
• Approximate Killing symmetries in non-perturbative quantum gravity
• Sharp estimate of lower bound for the first eigenvalue in the Laplacian operator on compact Riemannian manifolds

Cited by in corpus (1)

• Curvature effects in the spectral dimension of spin foams